Question

A man stands between two walls. He clapped his hands once and hears two echoes – one after 0.500 s and the other 0.300 s after the first. If the speed of sound in air is 330 ms-1, what is the distance between the two walls?

Answer

The first echo comes from the sound that travels to the nearer wall and reflects back.

The distance travelled by the sound is

Since the sound travels twice the distance between the man and the nearer wall,

The second echo comes from the sound that travels to the farther wall and reflects back.

We can calculate the distance travelled by the sound and the distance between the man and the farther wall.

Question

A molten alloy is made by mixing 450 g of molten cobalt of density 9.00 g/cm3 with 240 g of molten iron of density 8.00 g/cm3.

a) Calculate the density of the molten alloy in kg/m3.
(An important assumption must be made to do this question.)

b) What is the assumption made in your calculation?

c)Suppose now a 150 cm3 molten alloy of cobalt and iron has a density of 8.74 g/cm3, calculate the volume of cobalt and iron in the alloy in cm3. (You may make the same assumption as in previous parts of the question.)

Answer

a) To find the density of the molten alloy, we need to find the total mass and total volume of the alloy.

We assume that the two metals do not react and that the total mass is the sum of their individual masses and the total volume is the sum of their individual volumes.

b) We assume that the two metals do not react and that the total mass is the sum of their individual masses and the total volume is the sum of their individual volumes.

c) To find the volumes of iron and cobalt, we first need to find the mass of the molten alloy.

We can then write down the relationships between the total mass and the mass of the cobalt and iron.

Similarly we can write down an expression for the volume of cobalt and iron.

Since we know the density of iron and cobalt, we can use the density to link the masses to their respective volumes.

Question

A lamp is placed 30 cm above a metal surface which contains atoms of diameter 20 x 10-10 m. The lamp can be considered as a point source with power 0.015 W. It may be assumed that each electron can collect energy from a circular area which has a radius equal to that of the atom

a i) Find the intensity of the electromagnetic radiation directed on the atom.

ii) Hence, calculate the power incident on each atom.

iii) Determine, on the basis of wave theory, the time required for an electron to collect sufficient energy to be emitted from the metal if the work function of the metal is 3.2 x 10-19 J

iv) Comment on this calculation with actual experimental data and conclude the validity of wave theory.

Answer

a i) If we treat the lamp as a point source that emits light in all directions (3D),

Note that the area used is the total area which the power of the lamp is spread over.

aii) Now that we know the intensity of the light incident on the atom, we can calculate the power incident on the atom.

Note that the area used is the area of the atom which absorbs the power.

a iii) Since the electron requires a certain amount of energy to be emitted, we can calculate the time needed.

a iv) This calculation shows that if light were to be treated as a wave, the electron will required 7.68s to collect enough energy to be emitted. However, the experimental data shows that electrons will be emitted almost immediately, with a time much less than 7.68s.

This means that the wave theory cannot be used to describe the photoelectric effect.

Question

A breathing monitor consists of an 8-turn coil attached to a patient’s chest. As a breath is inhaled, the area of the coil varies from 0.120 m2 to 0.124 m2. The magnetic flux density of the Earth is 50 x 10-6 T and makes an angle of 22.5o with the axis of the coil.

If the patient inhales for 1.59s, what is the average emf induced in the coil during the inhalation?

A) 0.116 μV

B) 0.126 μV

C) 0.930 μV

D) 1.01 μV

Answer

To calculate the induced emf, the magnetic flux linkage of the coil has to be calculated.

Question

A displacement against position graph for a longitudinal wave is shown below. Which points represents the compressions and rarefactions?

Answer

For the graph, the position axis represents the location of the equilibrium position of a particle. The displacement axis gives the displacement of the particle from its equilibrium position. For this question, we assume that positive displacement is towards the right.

For example, in the graph below, Particle A has a equilibrium position at 0.80 m and it is displaced 1.5 mm to the right of its equilibrium position.

Question

In two widely-separated planetary systems whose suns have masses S1 and S2, planet P1 of mass M1 and planet P2 of mass M2 are observed to have circular orbits of equal radii respectively. If P1 completes and orbit in half the time by P2, it may be deduced that

A) S1 = S2 and M1 = 0.25 M2

B) S1 = 4 S2 only

C) S1 = 4 S2 and M1 = M2

D) S1 = 0.25 S2 only

E) S1 = 0.25 S2 and M1 = M2

Answer

For the system with S1 and P1, the gravitational force on P1 provides the centripetal force.

Similarly for the system with S2 and P2,

Since the period of P1 is half of P1,

Since the periods do not depend on the masses of the planets, we can only deduce that S1 = 4 S2.

Question

At a point outside the Earth and a distance of x from its centre, the Earth’s gravitational field strength is 5 N kg-1. At the Earth’s surface, the field strength is about 10 N kg-1. Which of the following gives an approximate value for the radius of the Earth?

A) x/5

B) x/2√2

C) x√2

D) x/√2

Answer

At point x, the gravitational field strength is given by the formula:

At the surface of the Earth, the gravitational field strength is given by the formula:

Question

A wire that obeys Hooke’s Law of length x1 when it is in equilibrium under tension T1. It’s length becomes x2 when the tension is increased to T2. What is the extra energy stored in the wire as a result of this process?

A) 1/4 ( T2 + T1 ) ( x2 - x1 )

B) 1/4 ( T2 + T1 ) ( x2 + x1 )

C) 1/2 ( T2 + T1 ) ( x2 - x1 )

D) 1/2 ( T2 + T1 ) ( x2 + x1 )

E) ( T2 - T1 ) ( x2 - x1 )

Answer

The extra energy is stored as elastic potential energy.

The graph of tension against total length is shown below. The extra elastic potential energy is given by the shaded area.

Question

Two containers of volume 4.0m3 and 6.0m3 contain an ideal gas at pressures of 100Pa and 50Pa respectively. Their temperatures are equal. They are joined by a tube of negligible volume. The gas flows from one container to the other with no change in temperature. The final pressure will be

A) 70 PaB) 75 PaC) 80 PaD) 150 Pa

Answer

Before the valve is opened, we first find an expression for the initial number of moles of gas in each container:

Now, the total initial number of moles of gas can be found:

After the valve is opened, the pressure in each container is now the same and the temperature remains the same.

The new expression for the final number of moles in each container is found again:

Question

A car travelling at a constant speed of 30 ms-1 passes a police car, which is at rest.

The police officer accelerates at a constant rate of 3.0 ms-2 and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the car moves past the police car.

What is the time required for the police officer to catch up with the car?

Answer

We assume that the police car catches up with the car at time t1.

The following formula for displacement can be obtained:

When the police car catches up with the car, both have travelled the same displacement.

Question

A child of mass 50 kg is on a swing which is suspended by 4.0m ropes from a rigid support. The horizontal speed of the swing as it passes through the lowest point is 3.0 ms-1.

What is the angle θ that the ropes make with the vertical when the swing is at the highest point?

Answer

We take the lowest point as the reference to measure the height of the child as he swings.

Since the lowest point is the reference level, the gravitational potential energy is 0 at the lowest point. As the child swings from the lowest point to the highest point, kinetic energy is converted to gravitational potential energy.

Using the value of h, we can find the length of the sides of the triangle.